Connected: An Internet Encyclopedia
RFC 1832 - APPENDIX A: ANSI/IEEE Standard 754-1985

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### APPENDIX A: ANSI/IEEE Standard 754-1985

The definition of NaNs, signed zero and infinity, and denormalized numbers from [3] is reproduced here for convenience. The definitions for quadruple-precision floating point numbers are analogs of those for single and double-precision floating point numbers, and are defined in [3].

In the following, 'S' stands for the sign bit, 'E' for the exponent, and 'F' for the fractional part. The symbol 'u' stands for an undefined bit (0 or 1).

For single-precision floating point numbers:

        Type                  S (1 bit)   E (8 bits)    F (23 bits)
        ----                  ---------   ----------    -----------
        signalling NaN        u           255 (max)     .0uuuuu---u
                                                        (with at least
                                                         one 1 bit)
        quiet NaN             u           255 (max)     .1uuuuu---u

        negative infinity     1           255 (max)     .000000---0

        positive infinity     0           255 (max)     .000000---0

        negative zero         1           0             .000000---0

        positive zero         0           0             .000000---0

For double-precision floating point numbers:

        Type                  S (1 bit)   E (11 bits)   F (52 bits)
        ----                  ---------   -----------   -----------
        signalling NaN        u           2047 (max)    .0uuuuu---u
                                                        (with at least
                                                         one 1 bit)
        quiet NaN             u           2047 (max)    .1uuuuu---u

        negative infinity     1           2047 (max)    .000000---0

        positive infinity     0           2047 (max)    .000000---0

        negative zero         1           0             .000000---0

        positive zero         0           0             .000000---0

For quadruple-precision floating point numbers:

        Type                  S (1 bit)   E (15 bits)   F (112 bits)
        ----                  ---------   -----------   ------------
        signalling NaN        u           32767 (max)   .0uuuuu---u
                                                        (with at least
                                                         one 1 bit)
        quiet NaN             u           32767 (max)   .1uuuuu---u

        negative infinity     1           32767 (max)   .000000---0

        positive infinity     0           32767 (max)   .000000---0

        negative zero         1           0             .000000---0

        positive zero         0           0             .000000---0

Subnormal numbers are represented as follows:

        Precision            Exponent       Value
        ---------            --------       -----
        Single               0              (-1)**S * 2**(-126) * 0.F

        Double               0              (-1)**S * 2**(-1022) * 0.F

        Quadruple            0              (-1)**S * 2**(-16382) * 0.F

Next: APPENDIX B: REFERENCES

Connected: An Internet Encyclopedia
RFC 1832 - APPENDIX A: ANSI/IEEE Standard 754-1985